Remark 2.3 Every nonlinear polynomial admits a long decomposition.
Part of Ritt's [1]} theorem on polynomial decompositions is
that the number \(k\)  depends only on the polynomial.
Of course, unless the polynomial is indecomposable,
the long decomposition itself is not an invariant, but the
rest of Ritt's theorem expresses the extent to which
it is and how one decomposition may be obtained from
another.

